@Article{weinkauf06a,
  author    = {T.~Weinkauf and H.~Theisel and H.-C.~Hege and H.-P.~Seidel},
  title     = {Topological Structures in Two-Parameter-Dependent {2D} Vector Fields},
  journal   = {Computer Graphics Forum (Proc. Eurographics)},
  year      = {2006},
  volume    = {25},
  number    = {3},
  pages     = {607--616},
  month     = {September},
  abstract  = {In this paper we extract and visualize the topological skeleton of
              two-parameter-dependent vector fields. This kind of vector data depends
              on two parameter dimensions, for instance physical time and a scale
              parameter. We show that two important classes of local bifurcations
              -- fold and Hopf bifurcations -- build line structures for which
              we present an approach to extract them. Furthermore we show that
              new kinds of structurally stable local bifurcations exist for this
              data, namely fold-fold and Hopf-fold bifurcations. We present a complete
              classification of them. We apply our topological extraction method
              to analyze a number of two-parameter-dependent vector fields with
              different physical interpretations of the two additional dimensions.},
  editor    = {E.~Gröller and L.~Szirmay-Kalos},
  keywords  = {vector field topology, 2D flow visualization, bifurcations, critical points, scale-space visualization, time-dependent visualization},
  url = {http://tinoweinkauf.net/publications/absweinkauf06a.html},
}